Q. 63

Expert-verifiedFound in: Page 202

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A 2.0 kg ball swings in a vertical circle on the end of an 80-cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is θ = 30^{o}.a. What is the ball’s speed when θ = 30^{o}?b. What are the magnitude and direction of the ball’s acceleration when θ = 30^{o}?

a) Balls speed is 3.85 m /sec

b) Ball's acceleration is 18.496 m/sec^{2}

Mass of ball is 2 kg

Length of string = 80 cm =0.8 m Tension in the string = 20 NWhen its angle from the highest point on the circle is θ = 30^{o}.

The centripetal force acting on a mass m revolving with speed v around a circle of radius r is given by

mv^{2}/r ……………………………….(1)

The centripetal acceleration is given by

v^{2}/r ……………………………….(2)

The tension of the spring at a given angle is and solve for v

Substitute the given value we get

Mass of ball is 2 kg

Length of string = 80 cm =0.8 mTension in the string = 20 NWhen its angle from the highest point on the circle is θ = 30^{o}.

The ball's radial acceleration is calculated as

Substitute the values given

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